A phase-integral perspective on alpha-decay

TL;DR

This paper employs the phase-integral method to analyze alpha-decay, providing rigorous connection formulae, accurate predictions for Uranium, and an original approximation for phase integrals across angular momenta.

Contribution

It introduces a rigorous application of the phase-integral method to alpha-decay, including new connection formulae and an original approximation for phase integrals.

Findings

Accurate prediction of Uranium's alpha-decay properties.

Development of a phase-integral algorithm for stationary states.

Introduction of an approximate formula for phase integrand with arbitrary angular momentum.

Abstract

This paper applies the phase-integral method to the stationary theory of alpha-decay. The rigorous form of the connection formulae, and their one-directional nature that was not widely known in the physical literature, are applied. The condition for obtaining s-wave metastable states affects the stationary state at large distance from the nucleus, which is dominated by the cosine of the phase integral minus (pi over 4). Accurate predictions for the lowest s-wave metastable state and mean life of the radioactive nucleus are obtained in the case of Uranium. The final part of the paper describes the phase-integral algorithm for evaluating stationary states by means of a suitable choice of freely specifiable base function. Within this framework, an original approximate formula for the phase integrand with arbitrary values of the angular momentum quantum number is obtained.